Will cellphone calls over wifi work when the power's out?

I'm considering cutting the landline cord. The ONLY reason I keep it is for emergencies. But cable phone service is $20 vs the $70 I pay for landline, so you see the concern.
Unfortunately, the cable phone only comes with an 8 hour battery backup. The battery backup is a proprietary (from what they tell me) battery that plugs into the phone modem with they install. Now, I have internet service through my cable provider as well. My phone supports calling over wifi. So, if I attached a UPS to my cable modem and router (the cable modem is a separate device from the phone modem), would I be able to call out on my cell phone in case of a power outage?
Also be advised that I found out during our last power outage that the cell towers also go down, so calling directly from my cellphone using my data plan was useless. My apologies for being a bit obsessive. But there's a huge gap between $20 a month and $70 a month.

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I did this!

We had a power outage and I used a power source (battery to AC) to power up our handy phones and it worked.

But you can't be sure that a power cut won't bring down the cell tower or other gear outside your home.

As such, when there's a city wide power outage, nothing can be assured about what will stay up. Here the cell towers have backup power for reasons. You may want to ask the carriers why they didn't stay up.

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Additonal Research confirms nothing can be assured

Thanks for your response. I've been researching since I posted this question, and truly, nothing's guaranteed in the event of a power outage other than the trusty landline. However, while I can't reduce my landline bill to match or beat the cable phone price, I did find out if I strip ALL features (voicemail, call-waiting, 3-way calling, etc), I could shave another $20 - $25 off the landline bill if a truly only wanted it as an emergency line.

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That's even in question.

An attack not long ago took out land lines as well. Maybe you can take the risk and if you need help, get in your car to go to some police or fire station like folk did not long ago.

There is no absolutely not going to go off line phone today. Maybe a satellite phone but woah, prices.

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Well if you have battery backup for

your modem and router then you would still be able to get to the internet to make or receive a call. That is unless your cable lines are down. Any cell phone can make calls over WIFI using apps like Skype, Whatsapp or Viber.

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